diff --git a/packages/@ot-doc/document/src/lib2/algebra.ts b/packages/@ot-doc/document/src/lib2/algebra.ts
new file mode 100644
index 0000000..3ed9b2e
--- /dev/null
+++ b/packages/@ot-doc/document/src/lib2/algebra.ts
@@ -0,0 +1,18 @@
+import { Maybe } from "./maybe";
+
+export type Constant<T> = () => T;
+export type UnaryOperator<T> = (a: T) => T;
+export type PartialUnaryOperator<T> = (a: T) => Maybe<T>;
+export type BinaryOperator<T> = (a: T) => UnaryOperator<T>;
+export type PartialBinaryOperator<T> = (a: T) => PartialUnaryOperator<T>;
+export type Predicate<T> = (a: T) => boolean;
+export type Relation<T> = (a: T) => Predicate<T>;
+
+// Use $PascalCase to represent a type class
+export type $Eq<T> = {
+  equals: Relation<T>;
+};
+
+export type $Ord<T> = {
+  lessThan: Relation<T>;
+};
diff --git a/packages/@ot-doc/document/src/lib2/document.ts b/packages/@ot-doc/document/src/lib2/document.ts
new file mode 100644
index 0000000..5470bae
--- /dev/null
+++ b/packages/@ot-doc/document/src/lib2/document.ts
@@ -0,0 +1,31 @@
+import { Constant, PartialBinaryOperator, PartialUnaryOperator, UnaryOperator } from "./algebra";
+
+export type $Init<Cp> = {
+  initial: Constant<Cp>;
+};
+
+export const $init = <Cp>(cp: Cp): $Init<Cp> => ({ initial: () => cp });
+
+export type $Comp<Cp, Op> = {
+  compose: (op: Op) => PartialUnaryOperator<Cp>;
+};
+
+export type $Inv<Op> = {
+  invert: UnaryOperator<Op>;
+};
+
+export type $Idn<Op> = {
+  identity: Constant<Op>;
+};
+
+export const $idn = <Op>(op: Op): $Idn<Op> => ({ identity: () => op });
+
+export type $Tran<Op> = {
+  transform: PartialBinaryOperator<Op>;
+};
+
+export type $BaseDoc<Cp, Op> = $Init<Cp> & $Comp<Cp, Op>;
+
+export type $InvDoc<Cp, Op> = $BaseDoc<Cp, Op> & $Inv<Op>;
+
+export type $FullDoc<Cp, Op> = $InvDoc<Cp, Op> & $Idn<Op> & $Tran<Op>;
diff --git a/packages/@ot-doc/document/src/lib2/maybe.ts b/packages/@ot-doc/document/src/lib2/maybe.ts
new file mode 100644
index 0000000..2612eac
--- /dev/null
+++ b/packages/@ot-doc/document/src/lib2/maybe.ts
@@ -0,0 +1,6 @@
+// $: Constructor type
+// v: the value
+export type Maybe<T> = { $: "Nothing" } | { $: "Just", v: T };
+
+export const nothing = <T>(): Maybe<T> => ({ $: "Nothing" });
+export const just = <T>(v: T): Maybe<T> => ({ $: "Just", v });
diff --git a/packages/@ot-doc/document/src/lib2/record.ts b/packages/@ot-doc/document/src/lib2/record.ts
new file mode 100644
index 0000000..6bcf0c8
--- /dev/null
+++ b/packages/@ot-doc/document/src/lib2/record.ts
@@ -0,0 +1,87 @@
+import { $Eq } from "./algebra";
+import { $BaseDoc, $FullDoc, $Idn, $InvDoc } from "./document";
+import { just, nothing } from "./maybe";
+
+export const $baseDocRecord =
+  <Cp>({ equals }: $Eq<Cp>) =>
+  <Op>({
+    initial,
+    compose,
+  }: $BaseDoc<Cp, Op>): $BaseDoc<Record<string, Cp>, Record<string, Op>> => {
+    const cpI = initial();
+
+    return {
+      initial: () => ({}),
+      compose: (op) => (cp) =>
+        Object.keys(op).reduce((cpT, key) => {
+          if (cpT.$ === 'Nothing') {
+            return cpT;
+          }
+          const cpK = cpT.v[key] ?? cpI;
+          const opK = op[key];
+          const mNewCpK = compose(opK)(cpK);
+          if (mNewCpK.$ === 'Nothing') {
+            return nothing();
+          }
+          const { v: newCpK } = mNewCpK;
+          if (!equals(newCpK)(cpK)) {
+            if (cpT.v === cp) {
+              cpT.v = { ...cp };
+            }
+            if (equals(newCpK)(cpI)) {
+              delete cpT.v[key];
+            } else {
+              cpT.v[key] = newCpK;
+            }
+          }
+          return cpT;
+        }, just(cp)),
+    };
+  };
+
+export const $invDocRecord =
+  <Cp>({ equals }: $Eq<Cp>) =>
+  <Op>({ initial, compose, invert }: $InvDoc<Cp, Op>): $InvDoc<Record<string, Cp>, Record<string, Op>> => {
+    return {
+      ...$baseDocRecord({ equals })({ initial, compose }),
+      invert: (op) => Object.keys(op).reduce((opT, key) => {
+        opT[key] = invert(op[key]);
+        return opT;
+      }, {} as Record<string, Op>),
+    };
+  };
+
+export const $fullDocRecord =
+  <Op>(clsOp: $Eq<Op> & $Idn<Op>) =>
+  <Cp>(clsCp: $Eq<Cp>) =>
+  ({ initial, compose, invert, transform }: $FullDoc<Cp, Op>): $FullDoc<Record<string, Cp>, Record<string, Op>> => {
+    const opI = clsOp.identity();
+
+    return {
+      ...$invDocRecord(clsCp)({ initial, compose, invert }),
+      identity: () => ({}),
+      transform: (opA) => (opB) => Object.keys(opA).reduce((mOpT, key) => {
+        if (mOpT.$ === 'Nothing' || !(key in opB)) {
+          return mOpT;
+        }
+        const opKA = mOpT.v[key];
+        const opKB = opB[key];
+        const mNewOpKA = transform(opKA)(opKB);
+        if (mNewOpKA.$ === 'Nothing') {
+          return nothing();
+        }
+        const { v: newOpKA } = mNewOpKA;
+        if (!clsOp.equals(newOpKA)(opKA)) {
+          if (mOpT.v === opA) {
+            mOpT.v = { ...opA };
+          }
+          if (clsOp.equals(newOpKA)(opI)) {
+            delete mOpT.v[key];
+          } else {
+            mOpT.v[key] = newOpKA;
+          }
+        }
+        return mOpT;
+      }, just(opA)),
+    };
+  };
diff --git a/packages/@ot-doc/document/src/lib2/singleton.ts b/packages/@ot-doc/document/src/lib2/singleton.ts
new file mode 100644
index 0000000..555a728
--- /dev/null
+++ b/packages/@ot-doc/document/src/lib2/singleton.ts
@@ -0,0 +1,51 @@
+import { $Eq, $Ord } from "./algebra";
+import { $FullDoc, $idn, $Init, $InvDoc } from "./document";
+import { just, nothing } from "./maybe";
+
+// f: update from value
+// t: update to value
+export type Update<A> = { f: A, t: A } | null;
+
+// Eq a => Eq (Update a)
+export const $eqUpdate = <A>({ equals }: $Eq<A>): $Eq<Update<A>> => ({
+  equals: (a) => (b) => {
+    if (a === b) {
+      return true;
+    }
+    if (!a || !b) {
+      return false;
+    }
+    return (equals(a.f)(b.f) && equals(a.t)(b.t))
+  },
+});
+
+// Eq a, Initial a => $InvDoc a (Update a)
+export const $invDocUpdate = <A>({
+  equals,
+  initial,
+}: $Eq<A> & $Init<A>): $InvDoc<A, Update<A>> => ({
+  initial,
+  compose:
+    (op) => op ? ((v) => equals(v)(op.f) ? just(op.t) : nothing()) : just,
+  invert: op => op ? { f: op.t, t: op.f } : null,
+});
+
+// Greater Write Win
+// Eq a, Initial a, Ord a => $FullDoc a (Update a)
+export const $fullDocGww = <A>({
+  equals,
+  initial,
+  lessThan,
+}: $Eq<A> & $Init<A> & $Ord<A>): $FullDoc<A, Update<A>> => ({
+  ...$invDocUpdate({ equals, initial }),
+  ...$idn(null),
+  transform: (opA) => (opB) => {
+    if (!opA) return just(null);
+    if (!opB) return just(opA);
+    const { f: fA, t: tA } = opA;
+    const { f: fB, t: tB } = opB;
+    if (!equals(fA)(fB)) return nothing();
+    return just(lessThan(tA)(tB) ? { f: tA, t: tB } : null);
+  },
+});
+
diff --git a/packages/@ot-doc/document/src/lib2/struct.ts b/packages/@ot-doc/document/src/lib2/struct.ts
new file mode 100644
index 0000000..e74da44
--- /dev/null
+++ b/packages/@ot-doc/document/src/lib2/struct.ts
@@ -0,0 +1,37 @@
+import { $Eq } from "./algebra";
+import { $BaseDoc, $FullDoc, $InvDoc } from "./document";
+
+export type Stt$Eq<T extends Record<string, unknown>> = {
+  [K in keyof T]: $Eq<T[K]>;
+};
+
+export type Stt$BaseDoc<Cp extends Record<string, unknown>, Op extends Record<keyof Cp, unknown>> = {
+  [K in keyof Cp]: $BaseDoc<Cp[K], Op[K]>;
+};
+
+export type Stt$InvDoc<Cp extends Record<string, unknown>, Op extends Record<keyof Cp, unknown>> = {
+  [K in keyof Cp]: $InvDoc<Cp[K], Op[K]>;
+};
+
+export type Stt$FullDoc<Cp extends Record<string, unknown>, Op extends Record<keyof Cp, unknown>> = {
+  [K in keyof Cp]: $FullDoc<Cp[K], Op[K]>;
+};
+
+export const $baseDocStruct = 
+  <Cp extends Record<string, unknown>>(stt$eq: Stt$Eq<Cp>) =>
+  <Op extends Record<keyof Cp, unknown>>(stt$baseDoc: Stt$BaseDoc<Cp, Op>): $BaseDoc<Cp, Op> => {
+    return {};
+  };
+    
+export const $invDocStruct = 
+  <Cp extends Record<string, unknown>>(stt$eq: Stt$Eq<Cp>) =>
+  <Op extends Record<keyof Cp, unknown>>(stt$invDoc: Stt$InvDoc<Cp, Op>): $InvDoc<Cp, Op> => {
+    return {};
+  };
+    
+export const $fullDocStruct = 
+  <Cp extends Record<string, unknown>>(stt$eq: Stt$Eq<Cp>) =>
+  <Op extends Record<keyof Cp, unknown>>(stt$fullDoc: Stt$FullDoc<Cp, Op>): $FullDoc<Cp, Op> => {
+    return {};
+  };
+    
\ No newline at end of file
diff --git a/packages/@ot-doc/document/src/lib2/timestamped.ts b/packages/@ot-doc/document/src/lib2/timestamped.ts
new file mode 100644
index 0000000..cf0086d
--- /dev/null
+++ b/packages/@ot-doc/document/src/lib2/timestamped.ts
@@ -0,0 +1,25 @@
+import { $Eq, $Ord } from "./algebra";
+import { $FullDoc, $Init } from "./document";
+import { $fullDocGww, Update } from "./singleton";
+
+// t: timestamp
+// v: value
+export type Timestamped<T> = { t: number, v: T };
+
+export const $eqTimestamped = <T>({ equals }: $Eq<T>): $Eq<Timestamped<T>> => ({
+  equals: (a) => (b) => a.t === b.t && equals(a.v)(b.v),
+});
+
+export const $ordTimestamped = <T>({ lessThan }: $Ord<T>): $Ord<Timestamped<T>> => ({
+  lessThan: (a) => (b) => a.t < b.t || (a.t === b.t && lessThan(a.v)(b.v)),
+});
+
+export const $fullDocLww = <A>(
+  cls: $Eq<A> & $Init<A> & $Ord<A>
+): $FullDoc<Timestamped<A>, Update<Timestamped<A>>> => {
+  const v = cls.initial();
+  const initial = () => ({ t: -Infinity, v });
+  const { equals } = $eqTimestamped(cls);
+  const { lessThan } = $ordTimestamped(cls);
+  return $fullDocGww({ equals, lessThan, initial });
+};